Discrete Math is very important in understanding how computers, hardware and software, work. All the circuits in a CPU are discrete functions, all the arithmetic and all operations are performed in binary values (binary values being boolean strings). It's also useful in theoretical computer science and the analysis of certain very hard problems as well as in the performance analysis of algorithms.
It will help you know what is going on, how your code works at the machine level, how it performs, what is the domain and range of your algorithms, etc.
From a programming perspective it is important to get you to understand Recursion, which very powerful and often used, and some basic stuff like Boolean math. Graphs also have a special place in computer science, but most of this stuff is straightforward, and plain common sense.